QuestionIs the Celsius temperature proportional to Fahrenheit? Use the formula $F = \frac{9}{5}C + 32$ for conversion.

Studdy Solution

STEP 1

Assumptions1. The conversion formula from Celsius to Fahrenheit is given by $= \frac{9}{5}C +32$ , where $$ is the temperature in Fahrenheit and $C$ is the temperature in Celsius. . We are asked to determine if the temperature in Celsius is proportional to its equivalent temperature in Fahrenheit.

STEP 2

To determine if two quantities are proportional, we need to check if the ratio of the two quantities remains constant. In this case, we need to check if the ratio of the temperature in Fahrenheit to the temperature in Celsius is the same for all temperatures.

STEP 3

We will calculate the equivalent Fahrenheit temperatures for the given Celsius temperatures using the conversion formula.
For $C =0$ ,
$= \frac{9}{5} \times0 +32$

STEP 4

Calculate the Fahrenheit temperature for $C =0$ .
$=0 +32 =32^{\circ}$

STEP 5

For $C =10$ ,
$= \frac{9}{5} \times10 +32$

STEP 6

Calculate the Fahrenheit temperature for $C =10$ .
$=18 +32 =50^{\circ}$

STEP 7

For $C =20$ ,
$= \frac{9}{5} \times20 +32$

STEP 8

Calculate the Fahrenheit temperature for $C =20$ .
$=36 +32 =68^{\circ}$

STEP 9

For $C =30$ ,
$= \frac{9}{5} \times30 +32$

STEP 10

Calculate the Fahrenheit temperature for $C =30$ .
$=54 +32 =86^{\circ}$

STEP 11

Now that we have the equivalent Fahrenheit temperatures for the given Celsius temperatures, we can calculate the ratios of Fahrenheit to Celsius for each temperature.
For $C =0$ , $=32^{\circ}$ ,
$Ratio = \frac{}{C} = \frac{32}{0}$

STEP 12

We see that the ratio for $C =0$ is undefined because we cannot divide by zero. This indicates that the temperature in Celsius is not proportional to its equivalent temperature in Fahrenheit.
The temperature in degrees Celsius is not proportional to its equivalent temperature in degrees Fahrenheit.

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QuestionIs the Celsius temperature proportional to Fahrenheit? Use the formula $F = \frac{9}{5}C + 32$ for conversion.

Studdy Solution

STEP 1

Assumptions1. The conversion formula from Celsius to Fahrenheit is given by $= \frac{9}{5}C +32$ , where $$ is the temperature in Fahrenheit and $C$ is the temperature in Celsius. . We are asked to determine if the temperature in Celsius is proportional to its equivalent temperature in Fahrenheit.

STEP 2

To determine if two quantities are proportional, we need to check if the ratio of the two quantities remains constant. In this case, we need to check if the ratio of the temperature in Fahrenheit to the temperature in Celsius is the same for all temperatures.

STEP 3

We will calculate the equivalent Fahrenheit temperatures for the given Celsius temperatures using the conversion formula.
For $C =0$ ,
$= \frac{9}{5} \times0 +32$

STEP 4

Calculate the Fahrenheit temperature for $C =0$ .
$=0 +32 =32^{\circ}$

STEP 5

For $C =10$ ,
$= \frac{9}{5} \times10 +32$

STEP 6

Calculate the Fahrenheit temperature for $C =10$ .
$=18 +32 =50^{\circ}$

STEP 7

For $C =20$ ,
$= \frac{9}{5} \times20 +32$

STEP 8

Calculate the Fahrenheit temperature for $C =20$ .
$=36 +32 =68^{\circ}$

STEP 9

For $C =30$ ,
$= \frac{9}{5} \times30 +32$

STEP 10

Calculate the Fahrenheit temperature for $C =30$ .
$=54 +32 =86^{\circ}$

STEP 11

Now that we have the equivalent Fahrenheit temperatures for the given Celsius temperatures, we can calculate the ratios of Fahrenheit to Celsius for each temperature.
For $C =0$ , $=32^{\circ}$ ,
$Ratio = \frac{}{C} = \frac{32}{0}$

STEP 12

We see that the ratio for $C =0$ is undefined because we cannot divide by zero. This indicates that the temperature in Celsius is not proportional to its equivalent temperature in Fahrenheit.
The temperature in degrees Celsius is not proportional to its equivalent temperature in degrees Fahrenheit.

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QuestionIs the Celsius temperature proportional to Fahrenheit? Use the formula F=95C+32F = \frac{9}{5}C + 32F=59​C+32 for conversion.

Studdy Solution

STEP 1

STEP 2

To determine if two quantities are proportional, we need to check if the ratio of the two quantities remains constant. In this case, we need to check if the ratio of the temperature in Fahrenheit to the temperature in Celsius is the same for all temperatures.

STEP 3

We will calculate the equivalent Fahrenheit temperatures for the given Celsius temperatures using the conversion formula.For C=0C =0C=0,=95×0+32 = \frac{9}{5} \times0 +32=59​×0+32

STEP 4

Calculate the Fahrenheit temperature for C=0C =0C=0.=0+32=32∘ =0 +32 =32^{\circ}=0+32=32∘

STEP 5

For C=10C =10C=10,=95×10+32 = \frac{9}{5} \times10 +32=59​×10+32

STEP 6

Calculate the Fahrenheit temperature for C=10C =10C=10.=18+32=50∘ =18 +32 =50^{\circ}=18+32=50∘

STEP 7

For C=20C =20C=20,=95×20+32 = \frac{9}{5} \times20 +32=59​×20+32

STEP 8

Calculate the Fahrenheit temperature for C=20C =20C=20.=36+32=68∘ =36 +32 =68^{\circ}=36+32=68∘

STEP 9

For C=30C =30C=30,=95×30+32 = \frac{9}{5} \times30 +32=59​×30+32

STEP 10

Calculate the Fahrenheit temperature for C=30C =30C=30.=54+32=86∘ =54 +32 =86^{\circ}=54+32=86∘

STEP 11

Now that we have the equivalent Fahrenheit temperatures for the given Celsius temperatures, we can calculate the ratios of Fahrenheit to Celsius for each temperature.For C=0C =0C=0, =32∘ =32^{\circ}=32∘,Ratio=C=320Ratio = \frac{}{C} = \frac{32}{0}Ratio=C​=032​

STEP 12

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QuestionIs the Celsius temperature proportional to Fahrenheit? Use the formula $F = \frac{9}{5}C + 32$ for conversion.

We will calculate the equivalent Fahrenheit temperatures for the given Celsius temperatures using the conversion formula.
For $C =0$ ,
$= \frac{9}{5} \times0 +32$

Calculate the Fahrenheit temperature for $C =0$ .
$=0 +32 =32^{\circ}$

For $C =10$ ,
$= \frac{9}{5} \times10 +32$

Calculate the Fahrenheit temperature for $C =10$ .
$=18 +32 =50^{\circ}$

For $C =20$ ,
$= \frac{9}{5} \times20 +32$

Calculate the Fahrenheit temperature for $C =20$ .
$=36 +32 =68^{\circ}$

For $C =30$ ,
$= \frac{9}{5} \times30 +32$

Calculate the Fahrenheit temperature for $C =30$ .
$=54 +32 =86^{\circ}$

Now that we have the equivalent Fahrenheit temperatures for the given Celsius temperatures, we can calculate the ratios of Fahrenheit to Celsius for each temperature.
For $C =0$ , $=32^{\circ}$ ,
$Ratio = \frac{}{C} = \frac{32}{0}$